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Slightly Nested FE

Source: 2nd Final Mathematical Cup Senior Division P1 (2020)

October 1, 2020
algebrafunctional equationFunctional EquationsFunctional equation in R

Problem Statement

Find all such functions f:Rā†’Rf:\mathbb{R} \to \mathbb{R} that for any real x,yx,y the following equation is true. f(f(x)+y)+1=f(x2+y)+2f(x)+2yf(f(x)+y)+1=f(x^2+y)+2f(x)+2y
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